the integration can be simplified to
∫ t⁻³ with the limits cosx and 0 (sorry it's difficult to type it >.<)
you then integrate the value to get:
∫ -1/2t⁻² with the limits cosx and 0
then sub in your limits to get;
( -1/2(cosx)⁻² ) - ( -1/2(0)⁻² )
= - cosx⁻² / 2
i hope this helps, if you're struggling to understand i can try get a written working out instead :D (not sure if i got this right too...)